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Worksheet by Kuta Software LLC

Honors Pre-Calculus

Trigonometry Test 1 Review

Name___________________________________

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-1-

Find a positive and a negative coterminal angle for each given angle.

1) 705°

345° and −15°

2) −230°

130° and −590°

3) 49π45

139π45

and −41π45

4) −π2

3π2

and −5π2

Find a coterminal angle between 0 and 2π for each given angle.

5) 35π12

11π12

6) 37π12

13π12

Convert each degree measure into radians and each radian measure into degrees.

7) 45°π4

8) −41π36

-205°

Find the length of each arc.

9) r = 17 yd, θ = π3

17π3

yd

10) r = 18 in, θ = 3π2

27π in

11) r = 13 mi, θ = 240°52π

3 mi

12) r = 16 cm, θ = 315°

28π cm

Find the exact value of each trigonometric function.

13) sec 30°

2 33

14) csc −330°

2

15) sin −3π4

−2

2

16) sin 5π6

12

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Worksheet by Kuta Software LLC-2-

17) cos 0

118) tan −

25π6

−3

3

19) cot −780°

−3

3

20) cot 0

Undefined

21) csc −7π2

1

22) cos −17π

3

12

Graph each function using radians. State the Amplitude, Period, Phase Shift, and Vertical Shift.

23) y = 4sin (θ − π2 )

π2

π 3π2

2π 5π2

3π

−6

−5

−4

−3

−2

−1

1

2

3

4

5

6

24) y = 1 + 3sin (θ3

+ π3 )

π 2π 3π 4π 5π 6π 7π 8π 9π

−6

−5

−4

−3

−2

−1

1

2

3

4

5

6

25) y = −1 + 2cos 4θ

−π4

π4

π2

3π4

π 5π4

3π2

7π4

2π

−6

−5

−4

−3

−2

−1

1

2

3

4

5

6

26) y = 3cos (3θ − π2 ) + 1

−π4

π4

π2

3π4

π 5π4

3π2

7π4

2π

−6

−5

−4

−3

−2

−1

1

2

3

4

5

6

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For the following questions determine the quadrant of ! if the angle is in standard position with 0 < ! < 2π

27. sin ! < 0 and tan ! > 0 28. tan ! < 0 and sin ! > 0

29. cos ! < 0 and csc ! > 0 30. sec ! < 0 and csc ! > 0

For the following questions point P is on the terminal side of angle !. Evaluate the six trig functions for !.

31. (-3, 6) 32. (12, 7)

33. ( -5, -3) 34. (4, 9)

35. Use a right triangle to determine the values of all trigonometric functions of !, where cos ! = 5/7

36. Find csc ! and cot ! if tan ! = -4/3 and sin ! > 0

37. Find sin ! and cos ! if cot ! = 3/7 and sec ! < 0

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38. A 14 foot ladder is used to scale a 13 foot wall. At what angle of elevation must the ladder be situated in order to reach the top of the wall?

39. From the top of a vertical cliff 40m high, the angle of depression of an object that is level with the cliff is 34 ̊. How far is the object from the base of the cliff?

40. A man flies a kite with a 100 foot string. The angle of elevation of the string is 52 ̊. How high off the ground is the kite?

For the following questions write the equation for the pictured graphs.

Use sine for graphs 41 and 42 and cosine for graphs 43 and 44.

41. 42.

43. 44.

13 414Sino _1,340 68.210

4omµ i4otan X_59.30MX an34

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X

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45. Researchers find a creature from an alien planet. Its body temperature is varying sinusoidally with time. 35 minutes after they start timing, it reaches a high of 120 ̊ F. 20 minutes after that it reaches its next low, 104 ̊ F.

A.) Write a sinusoidal function analytically that expresses temperature in terms of time (in minutes) since they started timing.

The function is: _______________________________________________________________________

B.) Find the first three times after they started timing at which the temperature was 114 ̊ F. _________________________________________________________________ 46. The following is the data for 24 hour average temperature for Florence, Italy for the average temperature measurements for the 12 months of several of the last few years. A.) Write a sinusoidal function analytically for the data B.) Write a regression equation

no

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Max

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1 C 7 TheOn testjus

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Cumulative Review: 47. Given f(x) = 3x – 5 and g(x) = x2, find the following: a) (A ° C)(D) b) C(A(2)) c) AYZ(D) d) CYZ(D) 48. Use the properties of logarithms to condense the following expressions. a) 2log a – 3log b + ½ log c b) 4log3 x – 6log3 y 49. Use the properties of logarithms to expand the following expressions. a) log` abcdef g b) lnh3\√Dk 50. Find the roots and state the multiplicity of each: What is the degree? ___ # of zeros? ____ # of possible extrema? ____ Actual # of extrema? ____ End Behavior? Write the linear factorization: 51. Write the equation of a fourth degree polynomial in expanded form with roots 3, -2, and -3 + i. Solve each equation algebraically and be sure to check for extraneous solutions. 52. 52.

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